Fluorescence microscopy is ubiquitous in biological studies because light can noninvasively probe the interior of a cell with high signal-to-background and remarkable label specificity. Unfortunately, optical diffraction limits the transverse (x-y) resolution of a conventional fluorescence microscope to approximately λ/(2NA), where λ is the optical wavelength and NA is the numerical aperture of the objective lens. This limitation may require that point sources need be more than about 200 nm apart in the visible wavelength region in order to be resolved with modern high-quality fluorescence microscopes. Diffraction causes the image of a single point emitter to appear as a blob (i.e., the point-spread function) with a width given by the diffraction limit. However, if the shape of the point spread function is measured, then the center position of the blob can be determined with a far greater precision (termed super-localization) that scales approximately as the diffraction limit divided by the square root of the number of photons collected, a fact noted as early as Heisenberg in the context of electron localization with photons and later extended to point objects and single-molecule emitters. Because single-molecule emitters are only a few nm in size, they represent particularly useful point sources for imaging, and super-localization of single molecules at room temperature has been pushed to the one nanometer regime in transverse (two-dimensional) imaging. In the third (z) dimension, diffraction also limits resolution to ˜2 nλ/NA2 with n the index of refraction, corresponding to a depth of field of about 500 nm in the visible with modern microscopes. Improvements in three-dimensional localization beyond this limit are also possible using astigmatism, defocusing, or simultaneous multiplane viewing.
Until recently, super-localization of individual molecules was unable to provide true resolution beyond the diffraction limit (super-resolution) because the concentration of emitters had to be kept at a very low value, less than one molecule every (200 nm)2, to prevent overlap of the point spread functions. In 2006, three groups independently proposed localizing sparse ensembles of photoswitchable or photoactivatable molecules as a solution to the “high concentration problem” to obtain super-resolution fluorescence images (denoted PALM, STORM, F-PALM, respectively). A final image is formed by summing the locations of all single molecules derived from sequential imaging of the separate randomly generated sparse collections. Variations on this idea have also appeared, for example, by using accumulated binding of diffusible probes, molecules whose emission blinks on and off, or quantum dot blinking Several of these techniques have recently been pushed to three dimensions using astigmatism, interfering multiple beams, and/or multiplane methods to quantify the z-position of the emitters. In the astigmatic case, the depth of field was only about 600 nm, whereas in the extensively analyzed multiplane approach, the maximum depth of field was about 1 μm. In the case of multiple beam interference, the optical configuration is complex and requires extreme stability.